There are multiple ways to get the extensions - RPMs if they exist, via the website, or as flatpaks. My bias is towards minimal installs and containerized apps, especially on Silverblue. TBH I’d prefer an OpenBox / i3wm Silverblue over a GNOME one.

Thank you! Now it’s working. System was successfully updated and Gnome Tweak installed. Now there’s another issue, though. Several GNOME extensions installed through Gnome Applications are not working (Dash to Dock among them). Gnome Tweaks says that there’s an error loading them (no description of error whatsoever). Other extensions (Screenshot tool, AppIndicator) appear to be working fine.
All of these extensions worked fine before Gnome Tweaks installed.

Dash to Dock has been finicky for me too - sometime it gives an error and I have to reboot to get it to work. There’s probably some state information that’s getting mangled / not cleared / not set properly.